Chemical computer

ABSTRACT

The invention provides a chemical computer having a matrix, an input device and an analytical device. The matrix is a plurality of interconnected reaction spaces holding a reaction mixture; the input device is provided to independently address each of a plurality of reaction spaces within the matrix; and the analytical device has a sensor to analyse a reaction characteristic of a reaction mixture in one or more reaction spaces. Also provides are methods for using the chemical computer, and the use of the chemical computer as a logic gate.

RELATED APPLICATION

The present case claims the benefit of, and priority to, GB 1815424.5filed on 21 Sep. 2018 (Sep. 21, 2018), the contents of which are herebyincorporated by reference in their entirety.

FIELD OF THE INVENTION

The present invention provides a programmable chemical computer for useas a logic gate and as a data store, as well as methods for operatinglogic gates and methods for storing and retrieving data using thechemical computer.

BACKGROUND

Over the last 50 years computers have become ubiquitous, essential formany aspects of modern life. During this period their processing powerhas increased manifold, but the paradigm used has remained the samekeeping the processor and memory separate (Toffoli), and using binarystate electronic switches. Systems based upon quantum effects promise tosolve problems intractable for conventional computers (Zhu et al.), butthey are yet to reach their full potential. However, nature exploits theparallelism of collective networks by developing systems able to processinformation despite large amounts of noise (Watts et al.; Deco et al.).

There is a desire for alternative systems of computing using alternativestrategies to process store and retrieve information that are low power,increase the number of computational states, and allow non-silicon-basedsubstrate for computation.

SUMMARY OF THE INVENTION

The present inventor has established that chemical reactions may beexploited for use in information processing, and more particularly,chemical reactivity may be reliably and repeatedly used within logicoperation and data storage.

In a general aspect the present invention provides a chemical computer,which utilizes individually addressable and addressed, but fullyinterconnected, reaction spaces within a matrix. The matrix holds areaction mixture which is capable of real time operation.

Addressing the reaction mixture held in one reaction space may give riseto the propagation of a reaction that extends into neighbouring reactionspaces. Consequential changes in the reaction mixture within thoseneighbouring spaces give rise to a detectable reaction characteristic.

The steps of addressing reaction spaces within the matrix, and theanalysis of reaction spaces for changes in reaction characteristics,allow the chemical computer to be used as a logic gate and also as adata storage and a data retrieval device.

In a first aspect of the invention there is provided a chemical computercomprising a matrix, an input device and an analytical device, wherein:

-   -   the matrix comprises a plurality of interconnected reaction        spaces holding a reaction mixture;    -   the input device is provided to independently address each of a        plurality of reaction spaces within the matrix; and    -   the analytical device has a sensor to analyse a reaction        characteristic of a reaction mixture in one or more reaction        spaces.

The reaction mixture may be a reaction mixture for a chemical oscillatorreaction.

The chemical oscillator reaction may be selected from the groupconsisting of a Belousov-Zhabotinsky (BZ) reaction, a Briggs-Rauscherreaction and a Bray-Liebhafsky reaction, such as a Belousov-Zhabotinsky(BZ) reaction.

The reaction mixture may be a reaction mixture having a colour change inits reaction, and here the analytical device has an optical sensor toanalyse the colour change in one or more reaction spaces. An oscillationreaction may therefore be oscillations between species of differentcolour.

The input device is for independently providing an input to each of aplurality of reaction spaces within the matrix. The input may beselected from the group consisting of a mechanical force, an opticalinput, an electrical input, a sonic input, a magnetic input and athermal input. Typically, the input device is for independentlyproviding a mechanical force to each of a plurality of reaction spaceswithin the matrix.

The invention also provides a logic gate which comprises the chemicalcomputer of the invention.

Furthermore, the invention also provides the use of a chemical computeras a logic gate.

The present invention also provides a method for the operation of achemical computer, for example for use as a logic gate or for use indata storage and retrieval, the method comprising the steps of:

-   -   (i) providing the chemical computer of the invention;    -   (ii) addressing a first and/or a second reaction space in the        matrix using the input device;    -   (iii) analysing a reaction characteristic of a third reaction        space using the analytical device;    -   (iv) determining a logic result based on the addressing step and        the analysis step.

SUMMARY OF THE FIGURES

FIG. 1 is a schematic of a chemical computer system according to anembodiment of the present invention, showing an illustration of (topleft) a digital domain represented by a matrix comprising a plurality ofdiscrete reaction spaces in a grid, which reaction spaces are addressedby mechanical stirring of the reaction mixture, with the option ofvariable speed; (top centre) a chemical domain, where the observedchemical reactivity in a reference matrix without discrete reactionspaces is shown (top) compared with the observed chemical reactivity ina matrix with discrete reaction spaces (bottom); (c) an analytical readout taken for a matrix where a selection of reaction spaces isaddressed, showing the raw recorded data (left), and the digitisation ofthe results based on a colour analysis of the reaction outcome, using,for example, machine learning processes (right); (bottom left) thechange in the number of possible computational states with the changesin the matrix size, as given by the total number of reaction spaces;(bottom middle) evolving microsites within a matrix, showing thatneighbouring reactions space may be regarded as weakly connected,oscillations will convolve, and be able to solve complex computations;(bottom right) a chemical recurrent state, showing that the BZoscillations have memory, therefore the global state of the reactionmedium not only depends on the input, but also on the state of previousiterations.

FIG. 2 shows (top left) a comparison matrix having limited connectivitybetween reaction spaces holding a reaction mixture for an oscillationreaction, and where specified reactions spaces are addressed (markedwith “x”) the observed changes in reactivity are substantially retainedin each of the addressed reaction spaces; (top right) a matrix havingreactive connectivity between reaction spaces holding a reaction mixturefor an oscillation reaction, a and where specified reactions spaces areaddressed (marked with “x”) the observed changes in reactivity are seento propagate into neighbouring reaction spaces; (bottom) changes in theobserved reactivity over time from the initial addressing of thereaction spaces (from first input at 0 s to 14 s), where the generationof coherent patterns was observed. A reaction mixture in a reactionspaces is addressed by mechanical perturbation of the reaction spaceusing a stirrer bar (when the stirrer bar is not enabled the matrix ismarked with “o”). Changes in the oscillation reaction at a local wereobservable as changes in the colour of the reaction mixture, which wasdetectable by a camera operating as an optical sensor.

FIG. 3 is a series of schematics of matrixes in a chemical computeraccording to an embodiment of the invention for use as logic gatesshowing the use (A) an AND gate; (B) and OR gate; and (C) an XOR gate,showing the truth tables for each operation. Each gate uses a matrixhaving a 5×5 arrangements of reaction spaces. A first series of reactionspaces at the left side (X) are addressable and a second series ofreaction spaces (Y) spaced from the left side is addressable. Thereaction mixtures within each reaction space are addressed by mechanicalperturbation of the reaction space using a stirrer bar. Shown in (A) and(B) are the recorded images where the first and/or second series ofreactions spaces is addressed. The distance between the series is usedto emulate the logic operation, owing to limited propagation of theexcitation wave from an addressed series of reaction spaces. If X and Yare separated by 4 reaction spaces, then the matrix behaves like an ANDgate, whereas if they are separated by 2 reaction spaces, then itbehaves like an OR gate. Shown in (C) are the recorded images where thelogical operation is based on a phase difference between localizedoscillations. The leftmost and rightmost five cells are considered asinputs (X, Y). The heat maps show the phase differences between thecentral cell (position 3,3) and other cells. E ach input pattern shows adistinctive BZ excitation wave pattern.

FIG. 4 is a series of schematics illustrating pattern classification anddata encoding using a chemical computer system, where (A) is a schematicfor BZ matrix data analysis using reservoir computing scheme; (B) is anexample output pattern of the BZ reaction system. The data after thetransition phase (μ15 min) was used for pattern recognition, which wasfurther split into two parts as training and test date, respectively;(C) is a schematic showing the full working pipeline of an embodiment ofthe invention. Initially the user selects a pattern to flash, and thispattern is binarised in 5 by 5 matrix. This matrix is used as a sourcefor the PWM generator, and this will eventually generate a globaloscillation. These oscillations are then encoded into a machine learningmodel, and decode when needed for pattern recognition; and (D) shows aBZ matrix and machine learning used for encoding data as an applicationexample.

FIG. 5 is a series of schematics comparing the use of a chemicalcomputer system with an autoencoder in a pattern recognition process,showing (top-left) a flow diagram of the pattern recognition process.The bottom path uses an Autoencoder which has been trained beforehand inorder to digitally produce BZ oscillations from motor patterns. The toppath uses the BZ medium as described on FIG. 4. In this case, thelabelling is performed by a Convolutional Neural Network (CNN) once theBZ oscillations are generated; (top-right) a diagram of the CNN used. Itcontained three convolutional layers with filters of 3×3, 5×5 and 3×3.In the bottom row there it can be seen how we speculate that the CNNlearns how to classify a given input by finding the points of theoscillations where it contains a bigger phase difference; and (bottom)digitally generated BZ oscillations using the Autoencoder. For eachcase, the input shown is the motor pattern used, and the output shown isthe BZ oscillation obtained. In these BZ oscillation plots the bluecolour represents when the oscillation happens. The X axis means time,and the Y axis means location—for each of the 25 reaction spaces. Thecoding represents the hidden layer of the Autoencoder.

DETAILED DESCRIPTION OF THE INVENTION

The present invention provides a digitally programmable chemicalcomputer, which comprises a matrix having independently addressable andinterconnected reaction spaces. The reaction spaces hold a reactionmixture, such as a reaction mixture for a chemical oscillating reaction,and this mixture is used as a data processing medium. The reactionmixture can be programmed to achieve flexible and multi-purposecomputation, by exploiting changes in the reactivity across the matrixin response to input signals delivered to certain reaction spaces withinthe matrix.

Addressing reaction mixtures held within the reaction spaces maygenerate spatiotemporal excitation patterns that extend across thematrix. In the preferred embodiments of the invention, a chemicaloscillation reaction is used, and the inputs into the matrix can be usedto control the oscillation at the addresses sites. Excited reactionwaves generated in a reaction space propagate to neighbouring cells andmay eventually form a globally synchronized oscillation pattern. As aresult, the platform is like the coupled-oscillator model (Crowley etal.). This type of reactivity provides for the use of the matrix withina programmable chemical computing system, exploiting the analoguedynamics of the chemical system.

The chemical computer is capable of performing different computationaltasks such as memory, logic operations and chemical autoencoding, forexample with pattern recognition.

The exemplification of the chemical computer in the present case uses areaction mixture for a chemical oscillating reaction, and specifically aBelousov-Zhabotinsky (BZ) reaction. The computer architecture is basedon data storage information processing via electron transfer betweenmolecules of [Fe(Bpy)₃]^(2/3+), and this depends on interactions betweenstates where the oxidized regions containing Fe(III) are blue, and thereduced states containing Fe(II) species are red. To achieve this, aplatform was designed that controls the oscillations of the BZ reactionat local reactions spaces, or sites, in a matrix by externallymanipulating the rotation speed of magnetic stirrers in the cells (amechanical manipulation of the cell contents), and using a camera abovethe matrix to monitor the oscillation states of the reaction in thecells.

Szymanski et al. have studied a Belousov-Zhabotinsky (BZ) reactionwithin aqueous droplets that are dispersed in an organic continuousphase. In particular, the authors have considered the transmission ofreactivity waves between neighbouring droplets, and they have looked atthe influence of droplet size on the transmission direction.

The work of Szymanski et al. does not make use of a matrix to hold eachreaction, and it does not describe the use of any device toindependently address each separate reaction. Seemingly Szymanski et al.generate droplets by simply dispersing the aqueous reaction phase in theorganic phase. In Szymanski et al. the droplets are allowed to form, anddifferences in reactivity between droplets result from differences indroplet size. The individual droplets used by Szymanski et al. are notindividually addressable in any way.

There is no suggestion by Szymanski et al. that their droplet systemcould be used as a logic gate or for data storage. Although Szymanski etal. say that their work is useful for information processing there is nodetailed description or example where the droplet system can be used inthis way.

Schinor et al. also consider a Belousov-Zhabotinsky (BZ) oscillationreaction, and how one reaction of this type might influence one or twoother reactions to which it is linked. The reaction set up in Schinor etal. uses two or three reaction vessels for each oscillation reaction,with each reaction vessel provided with a stirrer bar and anelectrochemical analytical device. The electrochemical signals recordedfrom one reaction vessel are transmitted to other reaction vessels andthe coupling of the oscillatory reactions in this way is analysed.

In the present case, a reaction within one reaction space is able topropagate a reaction wave from that space into a neighbouring reactionspace. Thus, there is a fluid connection between the reaction spaces,and this is not present in the system described by Schinor et al., whichrelies purely on electrical connections.

Adamatzky et al. discuss the use of the Belousov-Zhabotinsky (BZ)oscillation in logic operations. The work by Adamatzky et al. isentirely computational, and there is no in vitro experimental supportfor the in silico operation of the oscillation reactors described. Inparticular Adamatzky et al. do not explain how a reaction space can beaddressed in practice, and nor do they discuss the analysis of reactionoutcomes across a matrix.

Lebender et al. is earlier work from the same group as the Schinor etal. Lebender et al. describe the use of chemical reactivity to generatea logic gate capable of AND, OR and NAND operations.

The apparatus for use consists of a series of interlinked reactionvessels. Within the series there are two input reaction vessels for usein providing binary chemical signals: here two different reaction statesin a simplified version of the Belousov-Zhabotinsky (BZ) oscillationreaction. The reaction vessels are not in any way part of a matrix, andthey are used as separate reaction vessels.

Lebender et al. clearly explain that the interlinking between reactionvessels to form the logic gate is not a chemical interlinking, and thelogic operations are realised by computer operation. The authors explainthat a true chemical computer can only be achieved where the reactionoutcomes in the two input reaction vessels is fed to an output reaction,which is not the case in their work.

The present invention provides a chemical computer. Here is shown thatreaction waves initiated within input reaction spaces of a matrix arecan be propagated into neighbouring reaction spaces with constructiveand destructive interference giving a certain reaction result in thoseneighbouring spaces. This result can be read by an analytical device,and it gives the output for the logic operation (for example, as shownin FIG. 3 of the present case).

Chemical Computer

The chemical computer of the invention comprises a matrix, as describedherein, which is provided in combination with an input device and ananalytical device. Each of these components is described in furtherdetail below, together with their interoperation in logic processes andmethods for storing and retrieving data. The computer is programmable,as it is capable of accepting information, and is capable of storingthat information in the form of a modified chemical reactivity.

The chemical computer may further comprise a control unit forcontrolling the input device, for controlling the analytical device andfor interpreting the analytical data recorded by the analytical device.

The present invention also provides a plurality of chemical computers,where the chemical computers are provided in series or in parallel.

Matrix

The matrix is an array of interlinked reaction spaces. Each reactionspace may be referred to as an element or an entry within the matrix.

At its simplest, the matrix may be a sequence, such as a linearsequence, of elements. Thus the matrix may be regarded as substantiallyone dimensional. However, it is preferable that the elements arearranged in a grid. Thus the matrix may be regarded as two dimensional.In other embodiments, the elements may extend across three-dimensions.

The grid design may be adapted for the type of computation activityunder consideration. For example, in the operation of the matrix for alogic gate, the spacing between reaction spaces is important for thepropagation of reactivity through the matrix.

The matrix contains a reaction mixture, which mixture is distributedbetween reaction spaces of the matrix. The reaction mixture may be acontinuous reaction mixture throughout the matrix. Thus, the reactionspaces in the matrix do not substantially isolate portions of thereaction mixture. In practice, the matrix is provided with passages (orgates) between reaction spaces to allow for the continuous distributionof the reaction mixture through the array.

The reaction mixture may also be a series of contacting reactionmixtures, such as contacting droplets.

Chemical reactivity initiated in one reaction space may extend as areaction front (or wave) into neighbouring reaction spaces within thematrix. The reaction front may also be referred to as an excitationwave.

The dimensions and shape of each reaction space are not particularlylimited. In practice the volume of each reaction space is minimised,where possible, to minimise the size of the matrix itself, and thereforeto minimise the overall size of the chemical computer.

The shape of a reaction space is also chosen to allow for suitablepacking of neighbouring reaction spaces around it, and therefore toallow for reactive communication between neighbouring reaction spaces.

The effective memory, and the durability of the memory, can becontrolled by the amount of active reagents and the excitation route. Insimple terms, the larger the volume of chemistry, the longer thememories can be stored.

The programmability of the chemical computer is linked to the uniquenumber of reaction spaces in the matrix, which therefore also dictatesthe number of inputs that be made into the matrix. In addition to this,programmability is generated from the number of different chemicalstates that are accessible in response to the inputs, and thecombinations of inputs.

A reaction space is in reactive communication with its neighbours withinthe matrix. Thus, a reaction established in one reaction space ispermitted to propagate from that reaction space into neighbouringreaction spaces.

The reactive communication may be a fluid communication—typically liquidcommunication—between neighbours. Thus, individual reaction spaces maybe connected via fluid passages. On a practical level, the reactionspaces are provided by reaction chambers, whose walls are share withother reaction chambers. Walls between neighbouring reaction chambers,therefore neighbouring reaction spaces, may have openings to permitfluid communication between neighbours.

The fluid passages between neighbouring reaction spaces is sufficient toallow a reaction wave to be transmitted from one reaction space to itsneighbour.

One or more, and most preferably two or more, of the reaction spaces isaddressable by an externally applied force. The applied force is aninput for the system that is used to establish a reaction wave withinthe reaction space, which reaction wave is permitted to propagate intoneighbouring reaction spaces.

Preferably each of the reaction spaces is individually and independentlyaddressable.

The matrix is adapted for use with an input device, for applying a forceinto the reaction spaces.

The matrix is also adapted for use with an analytical device, foranalysing the contents of each of the reaction spaces.

The matrix may be a unitary piece, for example as might be formed byinjection moulding or 3D printing.

Input Device

The chemical computer is provided with an input device for applying aforce to one or more reaction spaces within the matrix. The matrix maytherefore be regarded as addressable by the input device. Essentiallythe input device is capable of independently perturbing each reactionspace in the matrix.

The input device is suitable for providing an input selected from thegroup consisting of a mechanical force, an optical input, an electricalinput, a sonic input, a magnetic input and a thermal input. Typically,the input device is for independently providing a mechanical force toeach of a plurality of reaction spaces within the matrix.

The input device may be capable of binary operation. Here, the inputdevice may provide a force, or provide no force at all. The input devicemay also be capable of providing degrees of force between a maximumforce and a minimum force, or no force.

The input device is suitable for providing an input continuously, or forperiods of time as necessary, and also intermittently as desired.

In the worked examples of the present case, a reaction mixture in aspace is addressed by mechanical force. Thus, a magnetic stirrer bar isprovided within each reaction space to provide mechanical agitation ofthe reaction mixture. The stirrer bar is a component of the inputdevice, which device is also provided with a plurality of magneticstirrers to independently operate each stirrer bar.

The magnetic stirrers are also used to demonstrate the use of the inputdevice to provide degrees of force to a reaction mixture within areaction space. As well as being capable of binary operation (on oroff), the stirrer speed may be altered to provide degrees of force, andthe worked examples shows how the changes that occur across a matrix inresponse to different magnitudes of force can be exploited, for examplein an XOR logic gate.

Analytical Device

The chemical computer is provided with an analytical device foranalysing the reaction spaces of the matrix.

The analytical device is provided with one or more sensors which arelocated about the matrix to permit the sensor to analyse the contents ofone or more reaction spaces. A sensor may be provided for each reactionspace, or alternatively a single sensor may be permitted to analyse aplurality of reaction spaces, such as all of the reaction spaces withinthe array.

The sensor is selected based on the reaction for performance, andparticularly the changes in the reaction mixture during a reaction.

The analytical device may comprise an optical sensor, an electrochemicalsensor, an acoustic, or combinations thereof. Typically the sensorshould be capable of 2D or 3D spatial mapping, and the time resolutionfor the sensor is preferably at a nanosecond level.

In the worked examples of the present case, the performance of thereaction is associated with a colour change, and an optical sensor isprovided to allow for the generation of a colour map across the array.

The analytical device may be provided with alternative sensors formeasurement of other characteristics of the reaction mixture.

In one embodiment the analytical device may be provided with a range ofsensors for detecting a plurality of characteristics of the reactionmixture.

The analytical device may comprise an optical sensor.

The data collected by the analytical device may be communicated to acontrol unit for analysis.

The analytical device may be controlled by the control unit. The controlunit may coordinate the measurement of analytical information with theinput.

The analytical device may be permitted to operate continuously to recordanalytical data from the reaction spaces.

Reaction Mixture

The matrix is provided with a reaction mixture, which is distributedacross a plurality of reaction spaces.

The reaction mixture typically comprises one or more reagents,optionally together with a solvent and optionally together with acatalyst. The reaction mixture may be a liquid mixture, such as asolution.

The reaction of the reaction mixture is associated with a change in adetectable characteristic of the reaction mixture, such as an opticalcharacteristic of the reaction mixture. The change in a characteristicof the reaction mixture is detectable by the sensor of the analyticaldevice.

Typically the reaction mixture is for a non-equilibrium reaction, forexample a reaction that is a non-equilibrium thermodynamic reaction.

The reaction mixture may be for a reaction that allows a large number ofchemical states to be accessed, but all these states can beinterconverted as a result of external operations.

The reaction mixture may be a reaction mixture for a chemical oscillatorreaction, a polymerisation reaction, a molecular synthesis, or anautocatalytic processes The reaction mixture may be a reaction mixturefor a chemical oscillator reaction. Such reactions are examples ofnon-equilibrium thermodynamic reactions.

When the reaction mixture is capable of periodic changes in theconcentration of one or more species within the mixture, additionalencoding can be achieved. Such an oscillator reaction may be initiatedor altered by application of an input to the reaction mixture, appliedby the input unit. In the present case, the oscillation is associatedwith a change in a characteristic of the reaction mixture that isdetectable by a sensor of the analytical unit. The oscillation may beassociated with a change in colour.

Where the reaction mixture is a chemical oscillator reaction, alocalised reaction mixture within a reaction space may be regarded as anoscillation clock. The methods of the invention may therefore look atchanges in the oscillation frequencies, which are influenced by theapplied force, where such a force is applied to a reaction mixture in areaction space.

In the absence of an applied input, a chemical oscillation localised ina reaction space may be essentially random, or chaotic, or not activatedat all.

However, when a reaction space is addressed, local order within thatreaction space may result. That local order may permeate, or propagate,from that reaction space into neighbouring reaction spaces. Analysis ofthe reaction spaces may show changes in the characteristics of thereaction that are associated with the propagation of the reaction fromone reaction space into another. This may be referred to as a reactionwave which is established by the applied force from the input device.

Where a plurality of reaction spaces are addressed, each of thesereaction spaces may set up a reaction wave that propagates beyond eachaddressed reaction space. A reaction mixture within a reaction space mayreceive a reaction wave from a neighbouring reaction space, and thatreaction space may receive a plurality of reaction waves from aplurality of neighbouring reaction space, for example providing aconstructive interference within the reaction space.

The chemical oscillator reaction may be selected from the groupconsisting of a Belousov-Zhabotinsky (BZ) reaction, a Briggs-Rauscherreaction and a Bray-Liebhafsky reaction, such as a Belousov-Zhabotinsky(BZ) reaction.

Other autocatalytic reactions can also be used, where the chemicalchange under consideration is reversible.

A BZ reaction may use bromine, for example as bromate.

In the present case, the reaction mixture may use an iron catalystwithin the Belousov-Zhabotinsky (BZ) reaction mixture, such as ironcatalyst oscillating between Fe(II) and Fe(III). The iron catalyst maybe ferroin, [Fe(bpy)₃]^(2/3+).

A chemical oscillation reaction may be a reaction which is chaotic inthe absence of an applied force.

A chemical oscillation reaction may be a reaction where the oscillationsare suppressed in the absence of an applied force.

A reaction in a reaction space may be initiated and optionally alsosustained by the application of a force into the reaction space.

The worked examples in the present case demonstrate show the use of anapplied mechanical force to a reaction mixture to initiate and sustain aBZ reaction.

The inventor has found that a reaction mixture within a reaction spacethat is addressed by the input device gives rise to a reaction wave thatextends from the reaction space into neighbouring reaction spaces. Thus,the change in the reactivity within a certain reaction space is capableof altering the reactivity of the reaction mixture in another reactionspace.

The reaction wave that is propagated from a reaction space typically hasa limited extent by which it can alter reactivity in neighbouringreaction spaces. The conditions under which a force is applied to areaction space may be selected to ensure that there is a limited extentof influence.

The present inventor has found that the propagation of a reaction intoneighbouring reaction spaces may be used as the basis for the operationof the chemical computer as a logic gate, for example as an OR gate.Similarly the limited extent of the propagation may also be exploitedfor operation of the chemical computer as a logic gate, for example asan AND gate. Logic operations are described in further detail below.

The inventor has also found that some reactions, such as oscillatingchemical reactions, retain a memory of their earlier perturbation, whichrefers to the earlier addressing of the reaction spaces by the inputdevice. Thus, a reaction pattern may persist in the matrix for a periodof time after an initial input into the matrix. In some embodiments, thememory may be permitted to degrade before further inputs are made intothe system. In other embodiments, further inputs are made into thesystem whist there is a persistence of an earlier reaction within thematrix.

Control Unit

The chemical computer may further comprise a control unit, which mayitself be a computer or a plurality of interlinked computers.

The control unit is suitably programmed to control the input device, forexample the control unit is capable of controlling which reaction spaceswithin the matrix are addressed, and the duration, and optionally alsothe degree, of the forces applied in the address.

The control unit is suitably programmed to control the analytical unit,for example the control unit is capable of instructing the analyticalunit which reaction spaces are to be analysed, and for how long. Thecontrol unit may also receive analytical data from the analytical unit,and it may analyse the analytical data.

A control unit may be used to control a plurality of matrices togetherwith associated input units and analytical units.

The control until may be the interface through which a user is capableof operating the chemical computer.

Logic Gate

The chemical computer of the invention may be a logic gate. The logicgate may be selected from the group consisting of AND, OR, XOR, NOT,NAND, NOR and XNOR logic gates. A chemical computer of the invention maybe capable of providing a plurality of logic functions, such as two ormore of those logic functions mentioned previously.

In preferred embodiments, the logic gate is selected from an AND, OR andXOR logic gate. The worked examples in the present case exemplify theuse of a chemical computer as a logic gate having AND, OR and XORfunctionality.

A logic gate may comprise a chemical computer comprising a matrix, aninput device and an analytical device, optionally also together with acontrol unit.

The matrix is adapted to function as a logic gate. Typically the inputdevice is available to provide inputs to selected reaction spaces in thematrix, such as one or a plurality of reactions spaces. The distributionof the inputs across the matrix, thereby to specifically address certainreaction spaces, provides a distribution of reactivity across thematrix, and that reactivity may be measured by the sensor of theanalytical device. The distribution of inputs to certain reaction spacesand the measurement of reaction outcome in other reaction spacesprovides are steps that define the logic operation of the chemicalcomputer.

The methods for operating a logic gate may include the step ofaddressing first and second reaction spaces in a matrix, where the firstand second reaction spaces are non-neighbouring reaction spaces, andanalysing a reaction mixture in a third reaction space, for examplewhere the third reaction space is provided between the non-neighbouringfirst and second reaction spaces.

In one embodiment, the third reaction space is provided between andneighbouring each of the first and second reaction spaces. Thisarrangement is suitable for use as an OR gate. Thus, the first to thirdreaction spaces are contiguous. Addressing reaction spaces in thisarrangement may be a part of a process of an OR operation in a logicgate.

Typically, where one of the first or the second reaction spaces isaddressed, a reaction wave is propagated from the reaction space, whichwave extends into the neighbouring third reaction space. The propagationof the reaction wave into that space gives rise to a reaction outcomethat is detectable. Thus, an input into first or second reaction spacesgive rises to a detectable signal.

Where both the first and second reaction spaces are addressed, thissimilarly gives rise to a detectable signal, in the third reactionspace, by propagation of reaction waves from both the first and secondreaction spaces into the third reaction space.

In one embodiment, the third reaction space is provided between each ofthe first and second reaction spaces, wherein the third reaction spacedoes not neighbour either of the first and second reaction spaces. Thisarrangement is suitable for use as an AND gate. Typically the thirdreaction space is separated from the first reaction space by one or morefurther reaction spaces, and similarly, the third reaction space isseparated from the second reaction space by one or more further reactionspaces. The reaction spaces, including the further reaction spaces maybe provided inline.

Typically, where one of the first or the second reaction spaces isaddressed, a reaction wave is propagated from the reaction space,however the reaction wave cannot significantly extend into thirdreaction space, and therefore there is no change or no significantchange in the characteristics of the reaction mixture within the thirdreaction space.

Where both the first and second reaction spaces are addressed, aplurality of reaction waves are propagated. Here, the combination of tworeaction waves into the third reaction space does give rise to asignificant change significant in the characteristics of the reactionmixture within the third reaction space.

The operation of the AND gate exploits the limited extent of thereaction wave to extend far across the matrix. Thus a single reactionwave at the limit of its extent, cannot significantly alter a reactionin a reaction space, such as the third reaction space. Only whenmultiple reaction waves propagate into a reaction space is there asignificant alteration in the reactivity, and this gives rise to adetectable signal.

The AND and OR gates may be operated in a system where the gates areoperated by inputs that may be on or off, corresponding to I and 0operations.

The operation of the XOR gate exploits differences in the reactionpatterns generated in the matrix when different magnitudes of force areapplied to specific reaction spaces. It has been found that logicoperations can be read from the observed reaction wave pattern acrossthe matrix.

As before, an XOR logic gate may comprise a matrix having first andsecond reaction spaces, which are typically non-neighbouring reactionspaces.

In the XOR logic gate operation, the first and second reaction spacesmay be addressed at different magnitudes of force (this is the I and 0input). This operation gives rise a reaction wave pattern across thematrix, which pattern is observed. In a symmetrical matrix withsymmetrical arrangement of the first and second reaction spaces, thewave pattern that is generated by addressing the first or the secondreaction space at different magnitudes of force is symmetrical.Typically the inventor has found that a bipolar wave pattern isgenerated.

The first and second reaction spaces may be addressed at the samemagnitude of force, which may be at higher force or lower force (thus,the inputs are 0 and 0, or I and I). These operations also gives rise toreaction wave patterns across the matrix, which patterns are observed.In a symmetrical matrix with symmetrical arrangement of the first andsecond reaction spaces, the wave pattern that is generated by addressingthe first or the second reaction space at the same magnitudes of forceis not symmetrical. Typically the inventor has found that differentnon-bipolar wave patterns are generated, where the same magnitude offorce is provided, at higher and lower force levels.

Thus, the XOR logic gate operation is based on the finding that thereactivity across the matrix differs in situations where the inputs arethe same and are different.

A plurality of logic gates may be connected, such as in series or inparallel, to allow for more advanced logic operations. The combinationsof logic gates in this way is well known to the skilled person.

Data Storage

The chemical computer of the invention may be used to encode informationthrough the use of a chemical reaction to provide a unique reactivitydistribution across a matrix.

The matrix of the chemical computer has independently addressablereaction spaces, each of which holds a part of the reaction mixture.Data may be chemically encoded into the matrix by appropriatemanipulation of the inputs. The chemical reactivity that results fromthe inputs addressing reaction mixtures within the matrix gives rise toa reactivity profile across the matrix, which profile may be recorded bythe sensor of the analytical unit.

In a simple operation, the input device is cable of binary operation foraddressing each reaction space within the matrix. Thus, the input devicecan apply a force to a reaction space or not apply that force. In theworked examples of the present case, a mechanical force is applied to areaction mixture by stirring of the mixture, and input device operateseither to stir or not stir a reaction mixture.

The application of a force to reaction mixture in a reaction spacechanges the reaction mixture, for example where oscillation reactionsare used, the input changes the oscillation of that reaction mixture.

Across the matrix the input device may operate to address selectedreaction spaces, thereby to change the oscillations of the reactionmixtures in those reaction spaces. The changes in the reactions, such asthe changes in the oscillations, may propagate from those reactionspaces into neighbouring reactions spaces, thereby affecting thereactions in those neighbouring reaction spaces also. Across the entirematrix this provides a particular reaction distribution the result ofwhich is detectable by the sensor of the reaction

For example, where a reaction is associated with a colour change, thereaction distribution across the matrix may give rise to a colourdistribution, which colour distribution may be recorded by an opticalsensor of the analytical unit. Such a system is exemplified in thepresent case.

The operation of the analytical device may be more complex than this, asthe application of the force may be graded, that is there is a spectrumof forces that may be applied to each reaction space, and the analyticaldevice may also be time controlled. Where the input device is capable ofdegrees of operation in relation to the forces it can apply, it followsthat a range of different reaction results may be accessed within areaction space, and these different reaction results in turn affect thepropagation of the reaction wave from the reaction space intoneighbouring reaction spaces. Thus different patterns of reactivity areaccessible across the matrix.

The inputs into the chemical space of the matrix may be seen as a forcepattern, which is a distribution of the applied forces to respectivereaction spaces. This then given rise to a reactivity pattern across thematrix, which is the change in the reactions across the space, resultingfrom localised changes within addressed reaction spaces, which give riseto reaction waves that extend into neighbouring reaction spaces. Theapplication of forces into the matrix generates a synchronized wavepattern.

Methods and Uses

The present invention provides the use of a chemical computer as a logicgate, and the use of the chemical computer as a data storage device. Theoperation of the chemical computer is as described above.

The chemical computer has programmability resulting from the discreteuse of individual inputs to reaction spaces within the matrix. Theseinputs give rise to reaction waves within the matrix that combine togenerate a unique reaction results that is the reactive response tothose inputs.

The inventor has found that the reaction result in the matrix isrepeatable for the same series of inputs. Thus the system is reliableand reproducible. The system can therefore recognise a particular outputthat is linked to a particular input.

Other Options

Each and every compatible combination of the embodiments described aboveis explicitly disclosed herein, as if each and every combination wasindividually and explicitly recited.

Various further aspects and embodiments of the present invention will beapparent to those skilled in the art in view of the present disclosure.

“and/or” where used herein is to be taken as specific disclosure of eachof the two specified features or components with or without the other.For example “A and/or B” is to be taken as specific disclosure of eachof (i) A, (ii) B and (iii) A and B, just as if each is set outindividually herein.

Unless context dictates otherwise, the descriptions and definitions ofthe features set out above are not limited to any particular aspect orembodiment of the invention and apply equally to all aspects andembodiments which are described. Where technically appropriateembodiments may be combined and thus the disclosure extends to allpermutations and combinations of the embodiments provided herein.

Certain aspects and embodiments of the invention will now be illustratedby way of example and with reference to the figures described above.

Examples

The following examples are provided solely to illustrate the presentinvention and are not intended to limit the scope of the invention, asdescribed herein.

Discussion

The exemplification of the chemical computer uses a reaction mixture fora chemical oscillating reaction, and specifically a Belousov-Zhabotinsky(BZ) reaction. The computer architecture is based on data storageinformation processing via electron transfer between molecules of[Fe(Bpy)₃]^(2/3+), and this depends on interactions between where theoxidized regions containing Fe(III) are blue, and the reduced statescontaining Fe(II) species are red. To achieve this, a platform wasdesigned that controls the oscillations of the BZ reaction at localreactions spaces, or sites, in a matrix by externally manipulating therotation speed of magnetic stirrers in the cells, and using a cameraabove the matrix to monitor the oscillation states of the reaction inthe cells.

The exemplified chemical computer consists of four components (see FIG.1).

(1) A matrix have 5×5 arrangement of reaction spaces, which may beregarded as reactor cell grid for the BZ reaction mixture, can becustomized to the desired geometry depending on the experiment. Inaddition, by changing the size of the opening gap between neighbouringreaction spaces it is possible to control the global propagation of BZexcitation (see FIG. 2). When the gap size was large enough, the wholeBZ medium generated coherent excitation wave patterns.

(2) A magnetic stirrer array consisting of 25 motors to control thestirrer bars placed within the individual BZ reaction spaces.

(3) An electronic control interface connected to a digital computer andthe magnetic stirrer array. The rotation speed of each stirrer wasindividually controllable therefore, the local oscillations of the BZreaction at a given cell could be individually addressed.

(4) The BZ reaction in the reactions spaces was monitored by a cameramounted above the grid. The camera was connected to a computer whichanalysed the BZ reaction in real time, and classified each cell asexcited (blue) or non-excited state (red).

Ferroin, [Fe(Bpy)₃]^(2/3+) was chosen as the sole catalyst since thisgives simple oscillations and the colour change between the reduced form(red) and the oxidized form (blue) is distinct and easily trackedoptically. The other chemical components used were hydrochloric acid,malonic acid and potassium bromate.

It is known that bulk oscillations of the BZ reaction break down and maybecome chaotic with short-lived or completely suppressed oscillationswhen they are not stirred (see Hsu et al.). This was exploited in thepresent system.

The excitation of an individual BZ reaction space in the matrix wascontrolled by activating a stirrer placed in that reactions space. Tostir reactions mixture within a cell, and to drive patterns in theresulting oscillations, the platform described in FIG. 1 was used, whereeach reaction space contained a stirring bar, and the reaction spaceswas located directly placed above a motor with a pair of opposingmagnets attached to its shaft. This way, the stirring could be turned onand BZ oscillatory excitation waves generated only in specific reactionspaces.

Defining which reaction spaces were addressed by stirring and which werenot (i.e. input pattern) could then impact the formation of excitationwave patterns on the chemical system. This is because the stirredreaction mixtures are more likely to generate oscillatory excited waves,which propagated to neighbouring cells and eventually formed a globallysynchronized wave pattern. The speed of stirrers in the matrix could beindividually controlled and input patterns with different stirrer speedscould result in different global wave patterns for the BZ reaction.

By using matrices of discrete but fluid-connected reaction spaces, itwas possible to control the propagation of wave patterns from a cell toa neighbouring cell. The basic starting design for the platformcomprised a 7×7 grid, where only the middle 5×5 cells were used.

To control the interaction between cells, we first designed a prototypearray of BZ cell grid using 3D printing which had a “v” shape openingbetween cells (FIG. 2B left). The BZ reaction volume used was 70 mL,which filled the arena to three quarters of its height, well above the“v” opening. With this design, it was found that oscillations did notpropagate to neighbouring reaction spaces and the platform actedsimilarly to a display screen, where only the reactions spaces that wereaddressed flashed in blue, while the other ones remained red (FIG. 2Top-Left)

To facilitate improved interaction between reaction spaces, wecompletely removed the “v” shaped part of the opening, leaving only thecorners of each cell to define it (FIG. 2 Top-Right). This way the fluidfrom an addressed reaction space would propagate to its neighbours whenstirred, and we could, for example, activate a reaction spaces that wasdisabled by stirring (and therefore activating) its neighbours.

The first objective was to emulate the behaviours of the simplest binarylogic gates since they form the basis of modern digital computers. Tobuild linearly separable binary logic gates, such as the “AND” and “OR”gates, we focused on the fact that BZ excitation waves generated at anactivated reaction space easily propagate to direct neighbours (i.e.distance=1), but very rarely propagate to cells further away (i.e.distance>1). By exploiting this feature, we designed 2-bit logic gatesusing the distance between inputs to implement “AND” and “OR” gates(FIGS. 3, A and B). When the distance between the two inputs (denoted asX and Y, respectively) is set to 3 and the output is set as the middlecolumn between them, our platform behaves like an “AND” gate, becauseoscillations in the output column are only observed when both inputs areactivated. On the other hand, when the distance between the inputs isset to 2 and column 2 is defined as output, then the system behaves likean “OR” gate, because whenever any of the inputs is enabled, theoscillations propagate to the output column.

To implement a non-linearly separable logic gate, such as “XOR”, weexploited the fact that when all of the stirrers were activated,globally synchronized wave patterns emerged from the system. Wespeculate that the emergence of globally synchronized patterns comesfrom two properties of the BZ reaction: (1) Sustained oscillation: onceactivated, a BZ reaction tends to sustain its oscillation even after thestirrer is off. Thus, each cell can be considered as an oscillator. (2)Signal convolution: the BZ excitation waves generated at a cellpropagate to neighbouring cells where another excitation waves aregenerated. The waves collide and interact to form a synchronizedoscillation. Thus, the whole BZ grid system can be viewed as a coupledoscillator system, or more in general, as a chemical dynamical systemthat consistently converts stirrer input patterns into patterns ofexcitation waves.

FIG. 3C shows how the XOR was implemented by exploiting the BZoscillations synchronization between cells. In this case, the ON/OFFbinary state of inputs employs two different stirrer speeds (ON for thefull speed and OFF for the slowest rotation speed possible), instead offully activating or disabling stirrers as we did before. In the BZ grid,the leftmost and rightmost five reaction space were considered asinputs, X and Y, respectively. If a column of five adjacent stirrers arerotated faster (the ON state), the stirrer motion generated aunidirectionally propagating wave pattern. This wave pattern was foundto be symmetric, thus both (0, 1) and (1, 0) inputs give mirrored wavepatterns. In contrast, the (0, 0) and (1, 1) inputs resulted indifferent yet reproducible wave patterns. To quantify these differentwave patterns, we calculated the phase differences between the centralcell and the other cells by cross correlation analysis (see FIG. 3C). Inparticular, (0, 1) and (1, 0) patterns show a bipolar pattern where oneside (“0” or non-activated side) shows positively shifted phase(indicated in red) while the other side (“1” or activated side) showsnegatively shifted phase because it was observed that excitation wavestend to propagate towards the cells with activated stirrers, thus thephase is delayed. On the other hand, the other cases, (0, 0) and (1, 1),showed different non-bipolar patterns. Therefore, the XOR gate can beimplemented by defining the bipolar wave pattern as output “1” and theother pattern as “0”.

To expand the computability of our system to perform more complex taskssuch as pattern recognition and data encoding, we interfaced ourchemical computer to an Artificial Neural Network, which was used ascomputing output layer to discover and discern the BZ computationalspace. The wave propagation patterns described before were found to bereproducible between parallel experiments, which indicates that our BZplatform can consistently convert an input pattern into a wavepropagation pattern. Detection and interpretation of such propagatingpatterns was relatively easy with simple input patterns, but itincreasingly becomes more complicated to human interpreters as the inputpatterns become complex. However, the complex patterns generated wereneither random, nor impossible to distinguish between them, because theBZ system generates consistent outputs in response to the same inputpattern.

To exploit this feature, we adapted the ‘reservoir computing’ schemeusing the BZ platform (FIG. 4, A) (Schrauwen et al.). Namely, thesystem's output is interfaced with a neural network which is used toclassify different input patterns based on the wave they generate. Thegenerated wave propagation patterns were input into a neural networklayer after being processed using image processing in order to identifythe BZ oscillations (FIG. 4, B). To capture the temporal dynamics of thewave propagation patterns, a sliding window over 100 time points (˜50seconds) was used to create a dataset with 2500 features (25 cells×100time points). We first used ten different input patterns representingdigital numbers from zero to nine with 1500 training data points and 300test data points, which gave correct answers with 98.6% accuracy againstthe test dataset.

This result suggests that the BZ system produces consistent patternsupon a specific input pattern that can be distinguished by a machinelearning algorithm (which may be too complicated for human eye). Inother words, the BZ system satisfies the “echo state property” ofreservoir computing (Yildiz et al.); i.e. each reaction space within its“reservoir” neighbours produces a nonlinear response signal which iscombined into a desired output signal by means of linear combinations ofthese response signals in the BZ matrix. It also should be noted thatthe system is capable of distinguishing similar patterns. For example,the pattern of number “2” and “3” are similar (one bit difference), butthe chemical computing system could easily distinguish them. We suspectthat this happens because the BZ reaction converts the input patternsinto a higher dimensional output space where the output neural networklayer is able to find a hyperplane that can distinguish differentinputs. In contrast, when using the reservoir system without the BZreaction, but replaced with pure water, the output neural network is notcapable of classifying the patterns because the dynamics of the waterare not sufficient to project input patterns into higher dimensionalspace.

To prove that during the pattern recognition process our BZ platformacted like a chemical computer, we performed a similar experiment, butin this case the BZ platform was replaced by a Fully-connected NeuralNetwork (in particular, an Autoencoder) which had been trained todigitally produce BZ oscillations from input motor patterns, see FIG. 5Top-left.

This way, the Autoencoder had as inputs the different motor patterns, itthen digitally generated a BZ oscillation, and then this BZ oscillationwas classified using a Convolutional Neural Network (CNN) (FIG. 5Top-Right). This is effectively the same process detailed in FIG. 4D,but by-passing the BZ medium and using a neural network instead. The CNNcorrectly labelled the different BZ oscillations, both the onesgenerated through the BZ medium, and the ones generated with theAutoencoder. This unequivocally means that our platform is acting like achemical computer because it is developing the same role as a neuralnetwork, specifically we can consider this to be acting like a chemicalautoencoder.

To bench mark the effective computational power of exhibited by the25-cell BZ system, we should consider the number of logical operationsthat the equivalent neural network would need to do in order to decodethe patterns, and how this is manifested in the silicon substrate. Giventhe BZ platform has 2²⁵ binary stirring pattern sates and around3.77×10²² chemical states, this seemed a reasonable challenge.Eventually it was possible to use an autoencoder that had three layersof 50-10-50 neurons, with 25 inputs for layer 1, 50 inputs for layer 2,and 10 inputs for layer 3 would give outcomes with similar accuracy. Thetotal number of operations can be evaluated to be of the order of 60 Moperations using around 32 M logic gates, which would need 100 Mtransistors. The total time the chemical-computer needed to decode thepattern is around 60 seconds worth of data which equates to around 1 Ms⁻¹.

This is believed to be the first time a chemical computer has beenbenchmarked, and it is shown that the complexity of the present systemcan be used to access a much larger computational space than then inputspace would allow.

The chemical computer of the invention serves as a sophisticated systemin which the dynamics or functions that are theoretically difficult toinfer can be calculated within the computation space defined by thelocalised reactivity within the chemical computer.

The chemical computer can be exploited as encoding device, and we havetested the described chemical encoding machine, and in our tests itcould distinguish a total of 26 patterns reliably, with up to 96%accuracy (see SI). This was achieved by addressing the cellsindividually, generating oscillations at localized positions, yet areweakly connected in a shared medium, creating a network of coupledoscillators, similar to, for example, the oscillatory neural computernetwork.²¹ In a 5×5 grid as defined, and in the case of binary stirrerinputs, there are a total of 2²⁵ (33554432) different states, althoughif we remove the binary restriction of the input, ourpulse-width-modulation generator can generate 3500 different signals,for a theoretical total of 3500²⁵ different states in the BZ computationspace.

Methods

Automated Platform

An automated platform was designed and built in order to perform theexperiments. The CAD design was done using OpenSCAD, and the pieces weremanufactured using the 3D-Printer “Stratasys Connex” and their material“VeroWhitePlus”. Each reaction space in the matrix platform contained astirrer bar (8×3 mm). Under each reaction space there was a geared DCmotor (6 V 200 RPM). These DC motors were controlled with a PWM signal.This PWM signal was generated using Arduino Mega, and the shield fromAdafruit “16-Channel 12-bit PWM/Servo shield—I2C interface”. A computerconnected to the Arduino board through USB ultimately defined thedifferent PWM signals through a Python script.

Preparation of Solutions

Ferroin Indicator: 0.025 M solution was prepared by dissolving 0.70 g offerrous sulfate heptahydrate and 1.5 g of 1,10-phenanthroline in 100 mLof water. Finally, 15 mL of this product were dissolved in 110 mL ofwater.

Potassium Bromate: 1M solution was prepared by dissolving 16.7 g KBrO₃in 100 mL of 1 M H₂SO₄.

Sulfuric Acid: 1 M H₂SO₄ was prepared by taking 5.6 mL conc. H₂SO₄ (96%,18 M) and adding to water to reach a total volume of 100 mL.

Malonic Acid: 1M solution was prepared by dissolving 10.4 g malonic acidin 100 mL 1M of H₂SO₄.

1M H₂SO₄ was sourced from Fisher Scientific, >95% analytical reagentgrade. Malonic acid was sourced from Sigma Aldrich, Reagent Plus 99%.Ferrous sulfate heptahydrate was sourced from Sigma Aldrich, >=98%.1,10-Phenanthroline was sourced from Sigma Aldrich, >=99%. Potassiumbromate was sourced from different sources. The main body of work ofthis research used the one sourced from Lancaster, 99%. Other suppliersused: Scientific Laboratory Supplies, 99% Alfa Aesar, 99.8% Alfa Aesarand Millipore Ensure.

Image Processing of Recorded Reaction Data

The experiments were recorded using a web camera (LifeCam Cinema,Microsoft) and saved as AVI videos using XVID compression, 800 by 600pixels and 30 FPS. OpenCV 3.4.1 and Python 3.6.5 were used. A datasetwas built were a human labelled different cells as red or blue. Intotal, 1541 cells were labelled as red, and 888 as blue. An SVM wastrained using this dataset. Each frame of a recorded video was processedby a pre-trained Support Vector Machine model to determine theactivation/non-activation state of BZ cells (cf. FIG. 1E). The SVMlibrary used was the one built into OpenCV. The activation state datacategorized by SVM was exported into a CSV file, in which the activatedstate was defined as “1” and the non-activated state as “0”.

Machine Learning for Chemical Reservoir Computing System

After the binary CSV file was generated, it was input into a machinelearning output layer of the chemical reservoir computing system. Forthe output layer, a multi-layered perceptron (MLP) was used. We used aMLP with only one hidden layer. Typically, 2500 input nodes and 200hidden layer nodes. The size of the final layer was changed depending onthe number of patterns to be classified. For activation function,rectified linear unit (ReLU) and softmax functions were used for thehidden and final layers, respectively. RMSprop was used for gradientdescent optimization algorithm with categorical cross-entropy as costfunction.

Accuracy of predictions were measured by “accuracy_score” function from“scikit-learn” library, which was defined as:

accuracy(ŷ,y)=1/NΣ _(i=0) ^(N−1)1(ŷ ₁ =y ₁)

-   -   where ŷ_(i) and y_(i) are the predicted and true values of i-th        sample, respectively. Computation was performed using a custom        code written in Python (version 3.6 from Anaconda 4.3.0). Keras        with TensorFlow backend was used to perform computation. A        graphical processing unit, GTX1060 with 6 GB memory, was used to        speed up the computation.

Convolutional Neural Network and Autoencoder

The Convolutional Neural Network (CNN) and Autoencoder implementationsfrom Tensorflow was used. Patterns representing numbers from 0 to 9 wereused. The CSVs used were the binarised ones. Therefore, each of theseCSV had values 0 to 1. These CSV contained 3600 columns values whichrepresented 30 minutes of experiment. In this case, rows from 1000 to3600 were used. The window size used was 25. Therefore, the inputs tothe CNN were 25 by 25, or 625 values. The test and train ratio were setto 30%. Three CNN layers were used. The first one uses 2 feature mapsand a kernel size of 3. The second one uses 2 feature maps and a kernelsize of 5. The third one uses 1 feature maps and a kernel size of 3.After this, there is a pooling layer, with 2 feature map and a kernelsize of 2. Finally, there is a fully connected layer with 16 neurons,and then 10 output neurons. The Autoencoder used had 25 inputs and 625outputs. Three hidden layers were used of 50, 10 and 50 neurons. Theautoencoder was trained using two cycles of 3000 iterations each. Thelearning rate was 0.000001 and L2 regularization was used (0.00001). Theinput of this autoencoder were 5 by 5 motor patterns, and its output of625 nodes was used as input to the CNN described.

Experimental Data

By using 3D printing to construct grids of discrete butfluidically-connected cells, we were able to control the propagation ofwave patterns from a cell to a neighbouring cell. The designs weremanufactured in a chemically resistant white plastic to allow the colourof each cell to be easily monitored. The basic starting design for thereactionware comprised a monolithic rectangular block into which asquare arena was inset. This was then divided into equal sized cells byprinting walls at equal spacings, with cut-outs in each wall to allowfluidic connection.

We first performed several pilot experiments to determine a suitablecell design that would produce sustained bulk BZ oscillation waves overthe whole cell, while being sufficiently large to be imagedconsistently. The best results were obtained using a 7×7 grid of 16×16by 5 mm cells where the cut-out accounted for a third of each connectingwall. Of the 7×7 grid, only the middle 5×5 cells were used forexperiments in order to avoid cells on the edges (with fewer neighbours)which might be expected to oscillate differently.

To control the interaction between cells, we first designed a prototypearray of BZ cell grid which had a “v” shape opening between cells andthe BZ reaction volume used was 70 ml, which filled the arena to threequarters of its height, well above the “v” opening. With this design, itwas found that oscillations did not propagate to neighbouring cells andthe platform acted similarly to a display screen, where only the cellsthat were enabled flashed in blue, while the other ones remained red.This demonstrated that our platform can act as a “display screen”. Inorder to test it, we used a static activation pattern of cells to flasha “smiley emoji” pattern and also sequenced pattern where columns wereactivated one after the other, left to right.

To facilitate improved interaction between cells, we completely removedthe “v” shaped part of the opening, leaving only the corners of eachcell to define it as fluid dynamics simulations showed that the removalof the barriers allowed the fluid from a stirred cell propagate toneighbouring cells upon stirring. This way, as can be seen in the 4-wayneighbourhood test, the fluid from an activated cell would propagate toits neighbours when stirred, and we could, for example, activate a cellthat was disabled by stirring (and therefore activating) its neighbours.

REFERENCES

All documents mentioned in this specification are incorporated herein byreference in their entirety.

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1. A chemical computer comprising a matrix, an input device and ananalytical device, wherein: the matrix comprises a plurality ofinterconnected reaction spaces holding a reaction mixture; the inputdevice is provided to independently address each of a plurality ofreaction spaces within the matrix; and the analytical device has asensor to analyse a reaction characteristic of a reaction mixture in oneor more reaction spaces.
 2. The chemical computer according to claim 1,wherein the reaction mixture is a reaction mixture for a chemicaloscillator reaction.
 3. The chemical computer according to claim 2,wherein the chemical oscillator reaction is selected from the groupconsisting of a Belousov-Zhabotinsky (BZ) reaction, a Briggs-Rauscherreaction and a Bray-Liebhafsky reaction.
 4. The chemical computeraccording to claim 3, wherein the reaction is a Belousov-Zhabotinsky(BZ) reaction.
 5. The chemical computer according to claim 1, whereinthe reaction mixture is a reaction mixture having a colour change in itsreaction, and the analytical device has an optical sensor to analyse thecolour change in one or more reaction spaces.
 6. The chemical computeraccording to claim 1, wherein the input device is for independentlyproviding an input to each of a plurality of reaction spaces within thematrix, wherein the input is selected from the group consisting of amechanical force, an optical input, an electrical input, a sonic input,a magnetic input and a thermal input.
 7. The chemical computer accordingto claim 6, wherein the input device is for independently providing amechanical force to each of a plurality of reaction spaces within thematrix.
 8. A logic gate which comprises a chemical computer according toclaim
 1. 9. The logic gate according to claim 8, comprising a pluralityof chemical computers according to claim 1, where the chemical computersare provided in series or in parallel.
 10. (canceled)
 11. A method ofoperating a chemical computer, the method comprising the steps of: (i)providing the chemical computer of claim 1; (ii) addressing a firstand/or a second reaction space in the matrix using the input device;(iii) analysing a reaction characteristic of a third reaction spaceusing the analytical device; (iv) determining a logic result based onthe addressing step and the analysis step.